Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11719426 | C2 | semidirect |
| 3. C13×#487 | C2 | semidirect |
| 4. #11718751 | C2 | semidirect |
| 7. #11718460 | C2 | semidirect |
| 9. #11718451 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 100. #487 | D13 | semidirect |
| 188. C13 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719437 | 2 |
| #11719426 | 2 |
| C13×#487 | 2 |
| #11718751 | 2 |
| #11718748 | 2 |
| #11718461 | 2 |
| #11718460 | 2 |
| #11718459 | 2 |
| #11718451 | 2 |
| C4×#6095 | 2 |
| C8×Dic26 | 2 |
| #3364 | 13 |